If I = J, then I, J is called a principal minor.The ( i, j) cofactor is obtained by multiplying the minor by ( − 1 ) i + j with k elements, then we write I, J for the k × k minor of A that corresponds to the rows with index in I and the columns with index in J. If A is a square matrix, then the minor of the entry in the i th row and j th column (also called the ( i, j) minor, or a first minor ) is the determinant of the submatrix formed by deleting the i th row and j th column. The requirement that the square matrix be smaller than the original matrix is often omitted in the definition.ĭefinition and illustration First minors Minors obtained by removing just one row and one column from square matrices ( first minors) are required for calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of square matrices. In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns. For the concept of "minor" in graph theory, see Graph minor. This article is about a concept in linear algebra.
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